Description Usage Arguments Author(s) References See Also Examples
This function computes the estimation of the density associated to the jump rate for a piecewise-deterministic Markov (PDMP) process whose state space is finite between the two times tmin and tmax. The estimator is given in the paper mentioned in References.
1 | CondPdf.DC.interval(dat,x,tmin,tmax,nbre,h,alpha,verbose,bound)
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dat |
data from which the estimator is to be computed. It corresponds to the observation of a PDMP within a long time. dat is a matrix such that the last column contains the interarrival times, while the other columns contain the states. |
x |
the conditional probability density function is estimated given state=x. |
tmin |
the conditional probability density function is estimated between tmin and tmax given state=x. |
tmax |
the conditional probability density function is estimated between tmin and tmax given state=x. In addition, tmax must be less than bound. |
nbre |
size of the grid plot. |
h |
bandwith |
alpha |
strictly positive real number. If h is NULL, the bandwith is 1/n^alpha where n is the number of data. |
verbose |
if TRUE, add a plot between tmin and tmax. |
bound |
the estimator is computed as an integral between the times 0 and bound. bound must be less than the deterministic exit time function tstar computed at state x. |
Romain Azais
Azais R., Dufour F., and Gegout-Petit A. Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes Scandinavian Journal of Statistics, 2014.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # CondPdf.DC.interval
# Simulation of a PDMP with discrete state space
dat<-Simu.PDMP.DC(1,500,verbose=FALSE)
# Estimation of the conditional density given state=2
CondPdf.DC.interval(dat,2,0.4,5.5,70,alpha=1/4,bound=5.8)
tmin<-0.4
tmax<-5.5
N<-70
a<-(N*tmin):(N*tmax)
a<-a/N
# Conditional density given state=2
gr<-exp(-a)
# Theoretical conditional pdf
points(a,gr,"l",col="blue")
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